At “semi-controlled” crosswalks, signs and markings are present, but delay to pedestrians and motorists is largely the result of the “negotiation” between the two parties to determine who yields. This paper proposes a novel approach using multi-state semi-Markov models to investigate motorists’ delay and their interactions with pedestrians. Motorist waiting behavior can be divided into a series of gap acceptance decisions as part of a Markov Chain. Each gap acceptance decision is modeled as a specific transition between two states in the Markov Chain.

To demonstrate the reliability of the proposed models, multi-state semi-Markov models are estimated for the waiting behavior of more than 1,000 drivers in the presence of pedestrians at semi-controlled crosswalks. The multi-state semi-Markov models are capable of dealing with specific challenges related to (i) the need to account for recurrent events and (ii) a generalized framework for vehicle delay estimation and simulation at semi-controlled crosswalks. The extent to which motorists behave more aggressively and impatiently as their delay increases is demonstrated. Differences in behavior for operators of buses and trucks were also identified. The semi-Markov method is also able to deal effectively with the “pulsing” arrival patterns of pedestrians at crosswalks as university classes begin and end nearby and handle temporal heterogeneity. Finally, to address aggressive driver behavior, several safety implications are discussed.

在“半控制”人行横道上，有标志和标记，但行人和驾车者的延误很大程度上是两方之间为确定谁屈服而进行的“谈判”的结果。本文提出了一种使用多状态半马尔可夫模型的新颖方法，以研究驾驶者的延误及其与行人的相互作用。作为马尔可夫链的一部分，驾驶者的等待行为可以分为一系列的差距接受决策。每个间隙接受决策都被建模为马尔可夫链中两个状态之间的特定转换。

为了证明所提出模型的可靠性，针对半控制人行横道上有行人的情况，针对1,000多名驾驶员的等待行为，估计了多状态半马尔可夫模型。多状态半马尔可夫模型能够应对与（i）考虑经常性事件和（ii）半控制人行横道上车辆延迟估计和仿真的通用框架有关的特定挑战。随着他们的延误的增加，驾车者表现出更积极和不耐烦的程度。还确定了公共汽车和卡车操作员的行为差异。当大学课程在附近开始和结束并处理时间异质性时，半马尔可夫方法还能够有效地处理人行横道上行人的“脉冲”到达模式。